Phase balancing is a classical optimization problem in power distribution grids that involve phase swapping of the loads and generators to reduce loss. The non-linear integer and, hence, it usually solved using heuristic algorithms. This paper proposes mathematical reformulation transforms phase-balancing low-voltage networks into mixed-integer convex quadratic model. To consider both conventio...

We consider the global optimization of nonconvex (mixed-integer) quadratic programs. present a family convex relaxations derived by convexifying functions through perturbations matrix. investigate theoretical properties these and show that they are equivalent to some particular semidefinite also introduce novel branching variable selection strategies motivated investigated in this paper. The pr...

Abstract A standard quadratic program is an optimization problem that consists of minimizing a (nonconvex) form over the unit simplex. We focus on reformulating as mixed integer linear programming problem. propose two alternative formulations. Our first formulation based casting with complementarity constraints. then employ binary variables to linearize For second formulation, we derive overest...

First, an integer programming model is proposed to find an α-labeling for quadratic graphs. Then, a Tabu search algorithm is developed to solve large scale problems. The proposed approach can generate α-labeling for special classes of quadratic graphs, not previously reported in the literature. Then, the main theorem of the paper is presented. We show how a problem in graph theory c...

Introduction. To minimise power loss, maintain the voltage within acceptable range, and improve quality in distribution networks, reconfiguration optimal distributed generation placement are presented. Power flow analysis advanced optimization techniques that can handle significant combinatorial problems must be used network investigations. The approach to depends on size of network. Our method...

This paper presents a novel mixed integer linear programing (MILP) formulation for finding the optimal layout of a fixed number of identical turbines that maximizes wind farm power generation. Previous MILP formulations with power maximizing objectives discretize the feasible space by using a grid of possible turbine locations. The proposed MILP formulation takes a different approach by allowin...

In this article, we propose a special case of two-echelon location-routing problem (2E-LRP) in cash-in-transit (CIT) sector. To tackle this realistic problem and to make the model applicable, a rich LRP considering several existing real-life variants and characteristics named BO-2E-PCLRPSD-TW including different objective functions, multiple echelons, multiple periods, capacitated vehicles, dis...

Inspired by the geometric reasoning exploited in discrete ellipsoid-based search (DEBS) from the communications literature, we develop a constraint programming (CP) approach to solve problems with strictly convex quadratic constraints. Such constraints appear in numerous applications such as modelling the ground-to-satellite distance in global positioning systems and evaluating the efficiency o...

We consider the Module Allocation Problem with Non-Uniform communication costs (MAPNU), where a set of program modules must be assigned to a set of processors. The optimal assignment minimizes the sum of execution costs and communication costs between modules. This problem is naturally formulated as a quadratic 0-1 problem with linear constraints. In this paper, we compare two exact solution me...